ACT Past Papers with Answers

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Which of the lollowing inatt'ices is equal to 3 14 i Ji 3 14 9 11 15 14 9 11 17 0 -14 86 59

A fiiiictioii, f, is detined by f(x,y)- 3x the vallle of f(4,3) 7 11 4y. 11.'hat is FI. 36 65

A certlliii gLOUP consists of 5 cIiildien, 3 of whom are Ige 10 cind 2 of whom &i"c agc 5. Ivhat is the meall age of the cliildren. iii tlie group.

In the figure sliowii below, AC11 DL; BD - AD: D and E ale on AB aiid BC, respectively. AC- 8 feet; and the Iieiglit of LABC is l O feet. Wh&È is DE, in feet? E 10 A •-8-IC Aryf-Al 1 -GO ON,TO-THE NEXT PAGE.

Iii tlie standard (x,y) coordinate p141ne, what is the slope oftheliiie4x+7y-9?

Wliit is tlia siiin ol the 2 solutions of the equation x'+x-30-07 -30 DO YOUR FIGURING HERE.

The voluine of. a sphere is where r is the radiuti of tlie spheie. What is tlie volume. in cubic Vards: ot a si)heie witli a dianzet61' of 4 yards? 32 47C 64 327C 48￿. 256

Wlial 18 tlie smallest integer watcr than V8) ? D, 12

The 3 statements below are true for the elements of sets A, B, C, and D. I. All elemeiit8 of A are elements of B. II. All elements of C Ell"e eleinents of D. Ill; No elerNenls of D aic elemenis of B. Which ot the followiiig state￿elllS must be true? Fl. Al L eleinents ol: C are eIkninenls of B. ,]. No eleilleiits of A (iie elemenrs of B. IC. No elements of A are eleinents of C.

In the staiidaid (x,y) Coordinate plane, the midpoint of AB is at (2,1), I nd A is at'(8.10).. What is the x-coordillale of B ? 17 GOONT .THE NEXT AGE.

Lena will pick I card at r&ndom froffl a pack of 25 baseball cards. Ecich card featUTes the fieldino position for l of 25 diffei-ellt baseball plavers. Each plclyer in the pack has only I fielding position. The table b¢low lists the frequency of fielthng positions in the p&clc. What is the piobability that the card Lena picks will featiire an outfielder or a pitcher? DO YOUR FIGURING HERE. Fielding position Frequency Catcher Infieldei" Pitchei OLltfielder 910

According to a soil ancilysis, a certain law.n requires an applicalion of 40.0 kg of nitTogen phosphate whcn the average tempei"aLLlI"e ig 75.O°F. To avoid bUrn￿g the grass, the required application amount decTeases

In ilie tiguie below, aIl segEnent.s that meet do 80 at right <2ngles. Wh¢1t is thc arca, in square units. ot the shaded region7 21, The perimeter of a certain scalene triar.gle is 100 inches, Tlie side Leiigths of the triangle arc represcnted by 5.T, 3x + 30, and Ir + 10, respectiwelv. What is the lengtli, in inches, of the longest side of th-e triangle? Acf.Al1 18 GO ON TO THE NEXT PAGE.

Source question 21. Refer to the source image.

Tlie iiiayoi of WesLbroolc is deciding how to assign the 6 council iiienibers to Ilie i.ow of seats below. DO YOUR FIGURING HERE. Fi"Dm how maiiy different arrangementb can she 21 36 64 720 IC. 6,000,000

The grapb iii the standaid (J,y) coordinate plane below is i'epreseiitcd by one of the following equations. Wliich equation? (02) I.1. y- (3.0) Il. y- _x+2

What is the aTea, in square feeL o.f the patio surroundin tbe pool,? 500 600 900

A full lap is 2 times the leiigth of the pool. Johann swani S full laps of die pool.in 4- minutes. Wliich of tlie following values is closest to Johann's average swiininiiig spced, iii feet pei minute? DO YOUR FIGURING HERE.

The gide view ot the i)ool is nlaced in the standard (x,Tr) coordinate plane, keeping the same oriLfntation and Sccile, sucli that botli vertical sesiiieiits showing depth arc parallel to Ilie y-axi,s. Which of the following values is closesl to tlie slope of the line seTrmcnt coniiecting the shallow end lo the deep end? -0.44 -0.63 -0.75

Shown below, cl board 5 feet 6 itLches long is cut inio 2 equal parls. What is t'he length. to the nearesi inch. of each Pr11t? DO YOUR FIGURING HERE. 5 feet 6 inclics A, 2 feet 5 inches D, 3 feet O inches

A company that builds bridges used a pile driver to drive a post into the ground. The post was driven 18 ftet into, th¢ ground by the fir<t hit.of the pile drivel. On each hit after tbe first hit, the post Wcls driven into the groiind an additional distance that iTras the distance the post was.drivell in the previoiis hit. After ll total of 4 hits, the post was driven hov¥ mallv teet into the ground?

In Lhe Stand￿'d (x,y) coordinate plane: A, is the image resulting from the reNknCtion of the poini .41 acKOSS the y-ax.is. NVhcTrt are the coordinates of .4, ? , (3,-2) ACT-A11 22 ONT THE NEXT P

To incLease tlie meclll of 4 nuinbers by. 3. by how much WOLild tlie sum ol. the 4 nllnibei￿ have to increase? DO YOUR FIGURING HERE.

Wliich OF the foIlowing expregsions ig equiN'alent to (3+x)- illo IDD io -300- IOOX 100 (3JJ IOD loo

Coiisidei the grapli of tlie eqliation y- in the stand(ird (x,y) cooi'dinate plane. Which of the foll0Th￿0 equ¢ltiong repregents the vertical asymptote of the graph7

Foi every pail ot re¢21 nuiiibers x and y such that.rJ: - and wliich of tlie following statements is true? x*Oaiidy-O Oandy*O i*Oandy#O of real nLimb¢rs x and y. ACT.A11 23 DO YOUR FIGURING HERE. Usg the following information to answer questions 38-40. Walter recently vaccltioned in Paris. While there. he Yisited the LoLivra, a f&tnous ait tllLi8eum. Afterward, he took a

Waltei"'s cab ride lasted 15 minutes. Which of the following valiies is closest to the average Spkned, in iLes per hour, of the Ci< b? (Note: I miIe -

When writtell in scientific notation, tlie number of rivets used to build the Eiffel Tower 18 equal to V¢hich of tlie following expressio￿￿?

At a certain point, the angle of elevation fornied by the level ground and the line froin that point to the top of the Eiffel Tower is 70°. Which of the tolloH:ing expre8sions is eqiial to tlie distance, in metk•rs, between that point and the centei of the base of the tower? FI. 320 tan 70° 320 sin 70° 320 tan 70°

When the vector ai + 3j is added to the vector-21 + bj: the sum is 61 - 6j. Whal al'e the valueb of a and b ? -9cindb= 8 aiidb 4andb- 8<lndb AGT-A11 24 GO ON TO THE NEXT PAGE.

Given c- IOb- + 50, wliich of the follov¥ing is an expi'ession for b in terms of c ? DO YOUR FIGURING HERE. 10 LO 10 (c- 50),

Givenf(x) - x, + 3x and g(x)- z + I, what isflgix)) ? x +5x+4 x +3x+l x +5x +4x x. +4x-+3x . K +4x +11

The diameter of oiie circle is 12 inches long. The diamelei of a second ciicle is 25% Jonger than the diattietei. of tlic fii&'t ciiclc, To the nearest square inch, how niuch largei is the area of the. second circle than the aiea of the first circle?

For all real values of x, which of the followin is triie? equations sin(71) + cos(7x) 7 sin(7x) + cos(71) siii'{7x) + cos (7x) 7 I<. sin'(7x) + cog (7x) ACT.A11 25 GO ON TO THE NEXT PAGE.

In tlie figui-e shown below. A, B, and D lie oll a circle whose cellter is Q, a diameter 1% AB. CD is perpendiciilar to AB clt C, the length ot AD is 5 m, and the length of BD is 12 ID. What is the length, in meters, ofcD? DO YOUR FIGURING HERE. 60 13 65 12 C, 13 156

If a aiid b are real numbers siich that a > O alld b < O. then wliich of the f:olIowing is equivalent to | a l - | b | ? |a+bl

If x < y and y < 4, then what is the gr=a' teit possible integei valiie of x + y

Sliowii belDW in ilie standai"d (XJ) coordinate plane are 2 cii".cles and l ellipse, eacli centered at (0.0). The larger cii.cle has equatson x + y - 25 and intersectf> Ilie ellipse at exactly 2 poiiits. both on the x-axis. Thc small.ei' circle lias eqiiaLion è + y 4 and illteisects the ellipse at exacily 2 points, both on Ihe y-axis. Wliich of tlie followiiig equations represents tbe ellipse? DO YOUR FIGURING HERE. 25 25

Tlie iriean OF 5 integers is 52. The median of tliese 5 inlegers is 82. Tliree of tlie integeis are 0, 12. and 82. Whicli of tlie f'ollowing could be one of the other integei-s? 86 53, An iiiteger is ab6¢ndani if Its positiye integLr factois, excludiiig the iiiLeger itself, h&ve a sum that Is great tlian the integer. How many of the integers 6. 8. 10. and 12 ale abundant?

Source question 53. Refer to the source image.

Source question 55. Refer to the source image.

Source question 56. Refer to the source image.

Source question 57. Refer to the source image.

Five balls, niimbered 1, 2, 3, 4, and 5, aie placed in a bin. Two balls ,ii-e drawn at random u'ithout repl£icement. WhriL is the prob&bility thiai Ihe sum ol tlie nLiinbers ot] tlie bic Ils clj.-awn is 7 ? 25 ACT-A11 28 GOONT THE NEXT PAGE.

Coiisidei the fllinily ot functioJ)s y -f(x) - sin x + c. wheie c is ¢1 real niiinbei. Wliich o-f the folloiving number lines i'epi'eseiiLg tlie giapli of all and only the possible vtilues of c f'or whiEh Lhe grdph of y has no x-iiitei'cepts ? DO YOUR FIGURING HE

Ta]nel<a calciilates that she needs 360 square fect of new carpet. But Lhe type of caypet that she wants is priced by the square ya.rd. How many square s:ard< of cai'pet does she need? 15 Fl. 60 END OF TEST2 STOP! DO NOT TURN THE PAGE UNTIL T DO NOT RETU LDTOD N TO THE PREVIOUS TEST. AGT-AI1 29